snap object by using its vertex as reference
In object mode, add an empty at the same location as the origin of the object:


Select the object, Snap Cursor to Selected 
Add Empty (will be at cursor location)


Snap the mesh to the Empty


Edit the Object and select all
Set Snapping to Vertex (with Closest option selected)
Grab the mesh and drag it to the Empty so that it snaps to it


[Edit]
If you need another vertex to be snapped to the empty you could instead set the Active option in the Snapping menu and have that vertex selected last. Or simply drag the mesh to a point where that vertex is the closest, release it and then snap it.